Long-term Capital Growth: The Good and Bad Properties of the Kelly and Fractional Kelly Capital Growth Criteria
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What they found
A balanced summary of what Kelly does and does not deliver, written by three of its leading proponents. The good: Kelly maximizes long-run growth, reaches any wealth goal in the shortest expected time, and never risks ruin in the idealized setting. The bad: the wealth path is extremely volatile, with drawdowns that most investors cannot stomach, and the strategy is very sensitive to errors in estimating the edge, so over-betting is a constant danger. They present simulations showing the distribution of outcomes for full, half, and quarter Kelly and argue that fractional Kelly offers most of the growth with far less pain.
What you can use
- Kelly's long-run promise comes with a short-run reality of huge swings; the median path is fine but the bad paths are brutal.
- Simulations show a fractional Kelly bettor gives up a modest amount of growth for a large reduction in the chance of a catastrophic drawdown.
- If your estimate of your edge is off by even a little, full Kelly becomes over-betting, and over-betting is where the ruin risk lives.
Caveats
Survey with simulations; relies on the same idealized independence assumptions. Written for a quantitative audience but readable.
Tags: risk, position-sizing, kelly, fractional-kelly, drawdown
Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.